How do you evaluate the limit #sqrt(x-2)# as x approaches #5#?

Answer 1
As #x# gets closer and closer to #5#,
#x-2# gets closer and closer to #5-2=3#, and
#sqrt(x-2)# gets closer and closer to #sqrt(5-2) = sqrt3#.
Yes, this is the same answer as what we get if we substitute #5# for #x#.

Be careful though! Not all limits can be found by substitution.

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Answer 2

To evaluate the limit of sqrt(x-2) as x approaches 5, we substitute 5 into the expression for x. This gives us sqrt(5-2), which simplifies to sqrt(3). Therefore, the limit of sqrt(x-2) as x approaches 5 is sqrt(3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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